{"ID":3005084,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T07:50:16.0004273Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03337","arxiv_id":"2606.03337","title":"Node-Oriented Proactive Spectral Modulation: A Unified Fractional Framework for Graph Signal Denoising","abstract":"Graph signal denoising is a fundamental task in graph signal processing. While the node-oriented filtering approach enhances spatial adaptability, it suffers from spectral rigidity due to its reliance on the graph Fourier transform. Conversely, emerging fractional-domain transforms provide crucial spectral flexibility but are fundamentally limited by their globally shared filtering paradigm, failing to accommodate localized topological variations. To bridge this gap, this paper proposes a generalized node-oriented fractional filtering (NOFF) framework that seamlessly integrates localized spatial adaptability with proactive spectral modulation across various fractional transforms. However, straightforwardly assigning independent full-rank filters to all vertices incurs a prohibitive parameter space, leading to severe overfitting on random noise. To mitigate this, we introduce the low-rank NOFF (LRNOFF) architecture. By imposing a strict low-rank constraint, LRNOFF inherently acts as a powerful implicit regularizer, preventing noise memorization and ensuring the extraction of robust spectral bases. Furthermore, we develop an efficient computational implementation termed LRNOFF-Fast, which drastically reduces computational and memory overhead while preserving theoretical optimality. Experiments on real-world datasets demonstrate that the proposed framework achieves state-of-the-art performance.","short_abstract":"Graph signal denoising is a fundamental task in graph signal processing. While the node-oriented filtering approach enhances spatial adaptability, it suffers from spectral rigidity due to its reliance on the graph Fourier transform. Conversely, emerging fractional-domain transforms provide crucial spectral flexibility...","url_abs":"https://arxiv.org/abs/2606.03337","url_pdf":"https://arxiv.org/pdf/2606.03337v1","authors":"[\"Manjun Cui\",\"Zhichao Zhang\",\"Yangfan He\"]","published":"2026-06-02T08:45:26Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}